Syllogism

high importance~3-5 Q in Tier 13 formulas⚡ 5 shortcuts4 subtopics

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Possibility conclusions

⏱ 5 min read🧩 5 question types🎯 12 practice Q

The idea in one minute

A possibility conclusion asks a lighter question: can this be true without breaking a statement? One supporting picture is enough to make it follow.

It fails only when a statement makes it impossible.

What a possibility conclusion asks

A definite conclusion says: this must be true. A possibility conclusion says: this can be true.

You are now looking for one picture only. If some picture fits every statement and also makes the possibility true, the possibility follows.

Rule: For a possibility, one supporting picture is enough. It follows unless a statement blocks it.

The one-picture method

Read the possibility as a request. For example: can I put all buses inside cars?
Try to draw it. Keep every statement true, especially every overlap.
If you can, it follows. If every attempt collides with a statement, it fails.

What blocks a possibility

A No statement. If no desk is a shelf, then no table inside desks can be a shelf.
A forced overlap. If every lion is a cat, no cat can fail to be a lion in all cases. 'No cat is a lion' is impossible.
Only a few. 'Only a few A are B' rules out 'All A are B'. It also rules out 'No A are B'.

Watch: Groups are never empty. So a possibility that empties a group always fails.

What stays possible

Most other cases stay possible. From 'Some A are B', all of these can be true: all A are B, all B are A, some A are not B.

From 'Only a few A are B', 'All B are A' is still possible. Draw B inside A and keep one A outside.

Two conclusions together

Often one conclusion is a possibility and the other is definite. Judge them by different standards. The definite one needs every picture. The possibility needs one picture.

Then match the pair to the options: only I, only II, both or neither.

Words that signal a possibility

Look for 'is a possibility', 'may be true' or 'can be true'. These words change the question from 'must' to 'can'.

Without them, treat the conclusion as definite.

A quick self-check

After you pick an answer, test it once. If you said a possibility fails, name the statement that blocks it. If you said it follows, name the picture that shows it.

Both answers should be easy to say in one sentence.

A worked example

Statements

Some cars are trucks.
Some trucks are buses.

Conclusions

I. All buses being cars is a possibility.
II. No cars are buses.

Options

(A) Only I follows
(B) Only II follows
(C) Both I and II follow
(D) Neither I nor II follows

Solution

For I, draw all buses inside cars. The car-truck overlap and the truck-bus overlap still hold. So I follows.
For II, cars and buses may overlap. So 'No car is a bus' is not forced, and II fails.

Answer: (A) Only I follows.

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common2 practice Q

Plain possibility (nothing blocks it)

How to spot it:

The words 'is a possibility' appear, and no 'No' statement touches the two terms.

Method

Try to draw the possibility around the statements.
Keep every 'Some' overlap alive.
If one clean picture survives, the possibility follows.

Why it works:

A possibility needs one consistent picture, not every picture.

Try this

Statements

Some cars are trucks.
Some trucks are buses.

Conclusions

I. All buses being cars is a possibility.
II. No cars are buses.

Options

(A) Only I follows
(B) Only II follows
(C) Both I and II follow
(D) Neither I nor II follows

Show solution

For I, draw all buses inside cars. The car-truck overlap and the truck-bus overlap still hold. So I follows.
For II, cars and buses may overlap. So 'No car is a bus' is not forced, and II fails.

Answer

(A) Only I follows

Type 2very common2 practice Q

Possibility blocked by a No statement

How to spot it:

A 'No X are Y' statement, and a possibility that would push X members into Y.

Method

Trace the members that are sure to exist.
Ask if the possibility would force one of them across the 'No'.
If yes, the possibility fails.
Test the partner conclusion separately.

Why it works:

A 'No' statement allows no crossing, whatever the picture.

Try this

Statements

All tables are desks.
No desks are shelves.

Conclusions

I. All shelves being tables is a possibility.
II. No shelves are tables.

Options

(A) Only II follows
(B) Both I and II follow
(C) Neither I nor II follows
(D) Only I follows

Show solution

Tables sit inside desks, and no desk is a shelf. So no table can be a shelf. II follows.
For I, all shelves would sit inside tables, and so inside desks. That breaks 'No desk is a shelf'. I fails.

Answer

(A) Only II follows

Type 3common2 practice Q

Possibility with only-a-few statements

How to spot it:

'Only a few A are B' and a possibility about A, B or a third group.

Method

Split it into Some and Some-not.
'All A are B' is now impossible.
Try to draw the other possibilities, such as 'All B are A'.
Keep the ones you can draw.

Why it works:

Only-a-few fixes the A side and leaves the B side open.

Try this

Statements

Only a few lamps are bulbs.

Conclusions

I. All lamps being bulbs is a possibility.
II. All bulbs being lamps is a possibility.

Options

(A) Only II follows
(B) Both I and II follow
(C) Neither I nor II follows
(D) Only I follows

Show solution

'Only a few lamps are bulbs' means some lamps are bulbs and some lamps are not bulbs.
I asks for all lamps to be bulbs. The lamp that is not a bulb blocks it.
II asks for all bulbs to be lamps. Draw bulbs inside lamps and keep one lamp outside. It works, so II follows.

Answer

(A) Only II follows

Type 4common2 practice Q

Possibility paired with a definite conclusion

How to spot it:

One conclusion is a possibility. The other is a definite claim.

Method

Test the definite one with a counter-picture.
Build one picture for the possibility.
Match the two results to the options.

Why it works:

The two halves use different standards.

Try this

Statements

All ships are boats.
Some boats are rafts.

Conclusions

I. All rafts being ships is a possibility.
II. Some ships are rafts.

Options

(A) Both I and II follow
(B) Neither I nor II follows
(C) Only I follows
(D) Only II follows

Show solution

For I, draw rafts inside ships, and ships inside boats. The boat-raft overlap still exists. So I follows.
II is a definite claim. The raft that is a boat may not be a ship. So II fails.

Answer

Type 5occasional

Possibility that empties a group

How to spot it:

After 'All A are B', a possibility such as 'No B are A'.

Method

Remember that every group has at least one member.
Every A is a B, so B and A meet.
Any possibility that separates them fails.

Why it works:

If groups cannot be empty, an All statement forces an overlap.

Try this

Statements

All lions are cats.

Conclusions

I. No cats being lions is a possibility.
II. Some cats being lions is a possibility.

Options

(A) Neither I nor II follows
(B) Only I follows
(C) Only II follows
(D) Both I and II follow

Show solution

Every lion is a cat, and lions exist. So at least one cat is a lion.
I needs no cat to be a lion. That is impossible, so I fails.
II is already true in every picture. So it is certainly possible.

Answer

Shortcuts that save time

⚡ Defence lawyer thinking

For a possibility, flip your mindset. Build one picture where it holds. Done.

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Looking for a picture where the possibility must hold.

You need only one picture where it can hold.

Mistake 02

Ignoring the 'No' statement when you draw the possibility.

A 'No' statement blocks every picture that puts a member across it.

Mistake 03

Saying 'No B are A' is possible after 'All A are B'.

Groups are non-empty. A member of A is a member of B, so B and A must meet.

Mistake 04

Saying 'All A are B' is possible after 'Only a few A are B'.

Only a few guarantees an A outside B, so that possibility is dead.

Mistake 05

Judging a definite conclusion by the one-picture rule.

A definite conclusion must hold in every picture.

Quick revision

Read this the night before the exam.

A possibility needs one supporting picture. A definite conclusion needs every picture.
A 'No' statement blocks a possibility that pushes a member across it.
Groups are non-empty. 'All A are B' makes 'No B are A' impossible.
'Only a few A are B' rules out 'All A are B' but leaves 'All B are A' possible.
Judge a mixed pair by different standards. Then match the options.

Practice: 12 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 12 questions

Suggested time 11 min · wrong answers go to your mistake notebook automatically.

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